Does the earth's moon have any gravity?
The Earth's moon does have its own gravitational pull. In fact, the gravitational pull of the moon is largely responsible for tides on Earth.
The gravitational pull of the moon can also be seen in the footage of the Apollo moon landings. Without any gravity, the astronauts and the moon landers would have floated off into space rather than staying on the Moon's surface.
All bodies - even those much smaller than the moon - have their own gravitational pull, but it is only strong enough to be noticed with very large objects such as asteroids, moons and planets.
The moon's mass is ~1% of the earth's, as such it's gravitational force is, at any given distance, 1% that of earths. If you compare surface gravity however, the moon's gravity is 1/6th (16%) that of earths, but this is because we are no longer measuring gravity at the same distance (earth's radius is:~6,300km while the moon's is: ~1,700km )